A224399 Numbers k such that A224166(k) = A008908(k).

1, 2, 4, 8, 13, 16, 26, 32, 35, 52, 64, 70, 81, 93, 104, 128, 140, 162, 181, 186, 208, 241, 256, 280, 324, 362, 372, 416, 455, 482, 483, 512, 543, 560, 607, 643, 645, 648, 724, 744, 809, 815, 832, 903, 910, 914, 915, 964, 966, 967, 1024, 1079, 1081, 1086, 1087

Offset

1,2

Comments

Numbers k for which the number of iterations starting with -k to reach the last number of the cycle equals the number of iterations starting with k to reach 1 in Collatz (3x+1) trajectory of +/-k.

Links

Table of n, a(n) for n=1..55.

Example

a(6) = 26 because A224166(26) = A008908(26) = 11.
The trajectory of - 26 is :
-26 -> - 13 -> -38 -> -19 -> -56 -> -28 -> -14 -> -7 -> -20 -> -10 -> -5 with 11 iterations (the first value is counted);
The trajectory of 26 is :
26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 with 11 iterations (the first value is counted).

Maple

z:={1}:
  for m from -1 by -1 to -1500 do:
   lst:={m}:a:=0: x:=m: lst:=lst union {x}:
        for i from 1 to 100 do:
         lst:=lst union {x}:
         if irem(abs(x), 2)=1
         then
         x:=3*x+1: lst:=lst union {x}:
         else
         x:=x/2: lst:=lst union {x}:
         fi:
         od:
         n0:=nops(lst):
         if lst intersect z = {1}
         then
         n1:=n0-2:
         else
         n1:=n0-1:
      fi:
       a:=0:y:=-m:
          for it from 1 to 100 while (y>1) do:
             if irem(y, 2)=0
             then
             y := y/2:a:=a+1:
             else
              y := 3*y+1: a := a+1:
             fi:
          od:
          if n1=a
          then
          printf(`%d, `, -m):
          else
          fi:
od:

Crossrefs

Cf. A008908, A224166.

Sequence in context: A268713 A363594 A320630 * A114398 A107326 A018671

Adjacent sequences: A224396 A224397 A224398 * A224400 A224401 A224402

Keyword

nonn

Author

Michel Lagneau, Apr 05 2013

Status

approved